We use the standard notation of Gudermann (see [1]}, p.494):
\(\sin \rm {am} (u,k) &=& \rm {sn}(u,k) \\\cos \rm {am} (u,k) &=& \rm {cn}(u,k) \\\sqrt{1-k^2 \, \rm {sn}^2(u,k)} &=& \rm {dn}(u,k) \mbox{ . }\) 
